### Abstract

The conditions for synchronization (equivalently, consensus) in linear and nonlinear switching dynamical systems have been extensively studied. In a previous study, we examined the speed of convergence of linear dynamical systems on switching networks in which each snapshot network defining interaction between dynamical elements is a network Laplacian. We showed that temporal dynamics (i.e., switching) of networks slowed down synchronization processes as compared to the case of aggregate dynamics, i.e., synchronization dynamics occurring on the corresponding static network obtained by the aggregation of the temporal network over time. Here we theoretically extend the results in two ways. First, we derive the conditions imposed on the interaction matrices under which the analytical slowing-down results hold true. The condition turns out to be essentially the same as that for the optimal network, which is known as the condition for the fastest local convergence of nonlinear dynamics on networks. Second, we examine the effect of correlation between different snapshots; in actual temporal networks, the same contact tends to be used consecutively in time. We argue that such temporal correlation further slows down temporal dynamics.

Original language | English |
---|---|

Pages (from-to) | 187-192 |

Number of pages | 6 |

Journal | IFAC-PapersOnLine |

Volume | 28 |

Issue number | 18 |

DOIs | |

Publication status | Published - Nov 1 2015 |

### Fingerprint

### Keywords

- Consensus
- Linear dynamics
- Spectral gap
- Switching dynamical system
- Synchronisation
- Temporal networks

### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

*IFAC-PapersOnLine*,

*28*(18), 187-192. https://doi.org/10.1016/j.ifacol.2015.11.034

**Slowing down of linear consensus dynamics on temporal networks : Some theoretical extensions.** / Masuda, Naoki; Klemm, Konstantin; Eguíluz, Víctor M.

Research output: Contribution to journal › Article

*IFAC-PapersOnLine*, vol. 28, no. 18, pp. 187-192. https://doi.org/10.1016/j.ifacol.2015.11.034

}

TY - JOUR

T1 - Slowing down of linear consensus dynamics on temporal networks

T2 - Some theoretical extensions

AU - Masuda, Naoki

AU - Klemm, Konstantin

AU - Eguíluz, Víctor M.

PY - 2015/11/1

Y1 - 2015/11/1

N2 - The conditions for synchronization (equivalently, consensus) in linear and nonlinear switching dynamical systems have been extensively studied. In a previous study, we examined the speed of convergence of linear dynamical systems on switching networks in which each snapshot network defining interaction between dynamical elements is a network Laplacian. We showed that temporal dynamics (i.e., switching) of networks slowed down synchronization processes as compared to the case of aggregate dynamics, i.e., synchronization dynamics occurring on the corresponding static network obtained by the aggregation of the temporal network over time. Here we theoretically extend the results in two ways. First, we derive the conditions imposed on the interaction matrices under which the analytical slowing-down results hold true. The condition turns out to be essentially the same as that for the optimal network, which is known as the condition for the fastest local convergence of nonlinear dynamics on networks. Second, we examine the effect of correlation between different snapshots; in actual temporal networks, the same contact tends to be used consecutively in time. We argue that such temporal correlation further slows down temporal dynamics.

AB - The conditions for synchronization (equivalently, consensus) in linear and nonlinear switching dynamical systems have been extensively studied. In a previous study, we examined the speed of convergence of linear dynamical systems on switching networks in which each snapshot network defining interaction between dynamical elements is a network Laplacian. We showed that temporal dynamics (i.e., switching) of networks slowed down synchronization processes as compared to the case of aggregate dynamics, i.e., synchronization dynamics occurring on the corresponding static network obtained by the aggregation of the temporal network over time. Here we theoretically extend the results in two ways. First, we derive the conditions imposed on the interaction matrices under which the analytical slowing-down results hold true. The condition turns out to be essentially the same as that for the optimal network, which is known as the condition for the fastest local convergence of nonlinear dynamics on networks. Second, we examine the effect of correlation between different snapshots; in actual temporal networks, the same contact tends to be used consecutively in time. We argue that such temporal correlation further slows down temporal dynamics.

KW - Consensus

KW - Linear dynamics

KW - Spectral gap

KW - Switching dynamical system

KW - Synchronisation

KW - Temporal networks

UR - http://www.scopus.com/inward/record.url?scp=84992507727&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84992507727&partnerID=8YFLogxK

U2 - 10.1016/j.ifacol.2015.11.034

DO - 10.1016/j.ifacol.2015.11.034

M3 - Article

AN - SCOPUS:84992507727

VL - 28

SP - 187

EP - 192

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

SN - 2405-8963

IS - 18

ER -